1. Field of the Invention
The present invention refers to a method for determining the three-dimensional surface of an object and a relevant computer program.
2. Description of Related Art
For describing and analysing the geometry of objects that have to be produced, modelling methods that use computers are known. In particular, when a three-dimensional surface enclosed by a set of points acquired from a real object has to be obtained, a technique called level-set that describes an enclosed surface as a level surface of a volumetric function (or implicit function) is normally used.
The level-set technique provides for the time evolution of the volumetric function, according to a suitable equation of the partial derivatives, typically belonging to the Hamilton—Jacobi family of equations.
The volumetric function describes the distance of each point from the enclosed surface and this distance will have positive or negative sign according to the point considered whether it is inside or outside the surface. Thus the set of points that possess a null distance from the surface S represent the surface itself. The technique provides for the evolution of the enclosed surface, defined by the Hamilton—Jacobi equation so that it surrounds and adheres to the cloud of 3D points that describes the object.
This technique is used as it is capable of adapting to the various types of objects and to the most diverse point acquisition techniques. This technique in fact, does not require any additional information about the topology of the points acquired and is insensitive to the technique used: the density of the points can vary in the different zones of the object considered; no information is required about the point acquisition sequence or about their relative spatial positions; and the number of objects enclosed separated from each other is not relevant for the algorithm.
As this technique requires the updating of a volumetric function at each step of evolution of the front, the calculation cost is usually very high, so much so that it makes the method of very little practical utility. Methods are known that permit the reduction of the calculation cost of this technique, for example limiting the updating of the volumetric function in an enclosed zone surrounding the front in evolution. Despite this the calculation cost remains prohibitive.
Alternative techniques to the level-set technique are also known. For example, methods such as those of the Delaunay triangulation are known, as well as the NURBS (Non Uniform Rational B-Splines) and the HRBF (Hierarchical Radial Basis Function). Each of these methods has limitations and imposes a series of restrictions on the set of the points acquired, such as for example the calculation complexity depends heavily on the number of points, or they need to have a spatial distribution of the points acquired as uniform as possible.